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If x, y, and z are different positive integers, is x prime?
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27 Jan 2015, 07:43
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66% (01:36) correct 34% (01:18) wrong based on 168 sessions
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If x, y, and z are different positive integers, is x prime? (1) xyz = 30 (2) z < x < y Kudos for a correct solution.
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Re: If x, y, and z are different positive integers, is x prime?
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27 Jan 2015, 08:52
Quote: If x, y, and z are different positive integers, is x prime?
(1) xyz = 30 (2) z < x < y y=/=x=/=z but all >0 and int. (1) > x could be 15 (z=1 and y=2) or 3 (z=5 and y=2) , its insuff. (2) > 100<200<300 (no prime) or 1<2<3 (prime!) > insuff. (1/2) > we need 3 distinct factors of 30 > 1/2/15 or 1/5/6 or 2/3/5 or 1/3/10 . every middle number is a prime, and since z is the smallest pos. int. and y the biggest pos. int., x is a prime number. C



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If x, y, and z are different positive integers, is x prime?
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27 Jan 2015, 09:07
ans C.. 1) it tells us that x is a divisor of 30..... x,y,z can be 1,2,3,5,6,10,15 2) insufficient..tells us x is middle value combined it tells us that x can be only 2,3,5 or 1,3,10, or 1,2,15 or 1,5,6 or .. so sufficient
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Re: If x, y, and z are different positive integers, is x prime?
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27 Jan 2015, 14:03
Bunuel wrote: If x, y, and z are different positive integers, is x prime?
(1) xyz = 30 (2) z < x < y
Kudos for a correct solution. 1) case_1 xyz=3*2*5 answer=yes; case_2 xyz=1*2*15 answer no. Not sufficient 2) Not sufficient 1+2) x is every time going to be a prime number. Sufficient Answer C.
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Re: If x, y, and z are different positive integers, is x prime?
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28 Jan 2015, 01:33
Here we go:
x, y, and z are different positive integers
St1: xyz = 30
30 = 2*3*5
x = 2, y = 3 and z = 5 (Is X prime? > true) x = 1, y = 6 and z = 5 (Is X prime? > false)
Not sufficient
St2: z < x < y
Clearly not sufficient
Combining both
z = 2, x = 3, y = 5 (Is X prime? > true) z = 1, x = 2, y = 15 (Is X prime? > true) z = 1, x = 5, y = 6 (Is X prime? > true) z = 1, x = 3, y = 10 (Is X prime? > true)
So C is the answer



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Re: If x, y, and z are different positive integers, is x prime?
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28 Jan 2015, 07:19
Bunuel wrote: If x, y, and z are different positive integers, is x prime?
(1) xyz = 30 (2) z < x < y
Kudos for a correct solution. Answer c: from stem: x,y and z are positive integers from 1: xyz = 30, prime factors of 30 are 1,2,3 and 5 consider xyz = 2*3*5 = 30 => x is prime, consider xyz = 6*5*1 = 30, x is not prime, 2 answers NSF from 2: z<x<y, considering only this statement, nohing is known, so NSF 1+2: z<x<y, the possible multiples are (note that z, x and y are written accordingly below) 1*2*15 = 30 1*5*6 = 30 1*3*10 = 30 2*3*5 = 30 are the only possible solutions and for all the solutions x is prime, so sufficient. C



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Re: If x, y, and z are different positive integers, is x prime?
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30 Jan 2015, 23:30
Quote: If x, y, and z are different positive integers, is x prime?
(1) xyz = 30 (2) z < x < y 1) X*Y*Z = 30 so X*Y*Z must be two factors of 30 * 1 X = 5, Y = 6, Z = 1: Yes X is prime X = 6, Y = 5, Z = 1: No X is not prime 2) Z<X<Y Z = 1 < X = 2 < Y = 3: Yes X is prime Z = 5 < X = 6 < Y = 7: No X is not prime 1+2) All possible pairs of factors of 30 are: (1,30) (2,15) (3,10) (5,6) but you can eliminate (1,30) from our choices because all numbers must be different. Thus ordered triples are: Z = 1 < X = 2 < Y = 15 Z = 1 < X = 3 < Y = 10 Z = 1 < X = 5 < Y = 6 Z = 2 < X = 3 < Y = 5 X = 2, 3, or 5, all of which are Prime. X is Prime, so C. Final Answer: C



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Re: If x, y, and z are different positive integers, is x prime?
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02 Feb 2015, 02:49
Bunuel wrote: If x, y, and z are different positive integers, is x prime?
(1) xyz = 30 (2) z < x < y
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION:Solution: C Let’s take statement (2) first: it gives us no values, so it’s INSUFFICIENT. Move on to statement (1). If three different positive integers have a product of 30, those integers must be one of the following sets:{ 1, 3, 10}; {2, 3, 5}; {1, 2, 15}; {1, 5, 6}. X could be prime or not prime; INSUFFICIENT. Combined, consider the four sets of possible integers. The median value is ALWAYS a prime number, so x must be prime. (C).
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Re: If x, y, and z are different positive integers, is x prime?
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07 Feb 2015, 05:20
[1] xyz = 30  NS because: 2*3*5 = 30, x prime 2*1*15 = 30, x prime 15*1*2 = 30, x not prime
[2] z<x<y  NS because: 2<3<6, x prime 3<8<10, x not prime
[1] and [2], S because: 1<1<30, x prime 1<2<15, x prime 1<3<10, x prime 2<3<5, x prime
So, there is no way for x not to be a prime, since, no matter what, y must be the greatest value of the 3 values that multilied together yield 30. Similarly, trying any factor of 30 (it has 8 factors: 1,2,3,5,6,10,15,30) there is no way that the middle one (x) will not be a prime.



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Re: If x, y, and z are different positive integers, is x prime?
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22 Aug 2018, 20:53
chetan2u wrote: ans C.. 1) it tells us that x is a divisor of 30..... x,y,z can be 1,2,3,5,6,10,15 2) insufficient..tells us x is middle value combined it tells us that x can be only 2,3,5.. so sufficient 1+2 combined: there should be 4 sets of combinations as stated in other posts. not just 2,3,5.




Re: If x, y, and z are different positive integers, is x prime?
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22 Aug 2018, 20:53






